In the past ten years, a flowmeter measuring the mass flow rate of media employing a single or a pair of vibrating conduits, that is commonly known as the Coriolis force or convective inertia force flowmeter, has become quite popular and scored a spectacular success in the field of industrial flow measurements. The existing versions of this mass flowmeter comprising the vibrating conduits of U-shaped, S-shaped or looped conduits are unreasonably expensive, and their design as well as construction are not suitable for the construction of mass flowmeters of a size greater than a 2 inch port diameter. The present invention teaches mass flowmeters employing a single or a pair of vibrating conduits, which provides an alternative to the existing versions of the mass flowmeter in terms of reduced cost, improved sensitivity and/or better feasibility in design to construct mass flowmeters of larger sizes.